Thermodynamic forces, flows, and Onsager coefficients in complex networks

Abstract

In this paper the linear theory of nonequilibrium thermodynamics, developed by Onsager and others, is applied to random networks with arbitrary degree distribution. Using the well-known methods of nonequilibrium thermodynamics we identify thermodynamic forces and their conjugated flows induced in networks as a result of single node degree perturbation. The forces and the flows can be understood as a response of the system to events, such as random removal of nodes or intentional attacks on them. Finally, we show that cross effects (such as thermodiffusion, or thermoelectric phenomena), in which one force may not only give rise to its own conjugated flow, but to many other flows, can be observed also in complex networks.